Graph of horizontal asymptote

Question

The graph of f(x) has a horizontal asymptote y=5.

 

1. What is the horizontal asymptote of the graph of f(x)+5?

 

2. What is the horizontal asymptote of the graph of f(x+5)?

Answer 1

1.  H.A. is y=10 because the new function is the result of a vertical shift upward by 5 units.

 

2. Horizontal asymptote is unchanged, because H.A. is based on x approaching infinity, which approach is immaterially changed when approaching infinity + 5